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A note on Bayesian analysis in \(M/M/1\) queues derived from confidence intervals. (English) Zbl 0893.62019

Summary: The purpose of this paper is to use the implied likelihood introduced by B. Efron [Biometrika 80, No. 1, 3-26 (1993; Zbl 0773.62021)] for making Bayesian inference about the traffic intensity \(\rho\) in an M/M/1 queue, without worrying about nuisance parameters. A comparison with the posterior distribution of \(\rho\) obtained by C. Armero and M. J. Bayarri [Tech. Rep. 10-92, Opt. Stat. Oper. Res., Univ. Valencia (1992)] is considered.

MSC:

62F15 Bayesian inference
62M99 Inference from stochastic processes
62F25 Parametric tolerance and confidence regions

Citations:

Zbl 0773.62021
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References:

[1] Armero, C. and Bayarri, M. J. 1992a. ”Bayesian prediction in M/M/1 queues”. Department of Statistics and Operations Research, University of Valencia. Tech. Rep., 9–92
[2] Armero, C. and Bayarri, M. J. 1992b. ”Prior assessments for the prediction in queues”. Department of Statistics and Operations Research, University of Valencia. Tech. Rep., 10–92.
[3] Cox D. R., J. R. Statist. Soc. 49 pp 1– (1987)
[4] DOI: 10.1093/biomet/80.1.3 · Zbl 0773.62021 · doi:10.1093/biomet/80.1.3
[5] Gross D., Fundamentals of queueing theory (1985) · Zbl 0658.60122
[6] DOI: 10.1007/978-1-4612-1096-2 · doi:10.1007/978-1-4612-1096-2
[7] DOI: 10.1214/ss/1177011232 · Zbl 0955.62522 · doi:10.1214/ss/1177011232
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